401(k) and similar plans have the option to refuse receiving rollovers. Keep in mind that you can only roll over to a 401(k) or similar plan the otherwise taxable amount of the offset distribution (usually the entire amount). You can roll over to an IRA the taxable and nontaxable nontaxable amounts. The code M Form 1099-R that you receive for the offset distribution will indicate the taxable amount in box 2a.
You must follow the rollover procedures of the receiving plan or IRA custodian. In the case of a rollover of an offset distribution you must tell the receiving plan or IRA custodian, generally using their rollover contribution form, that it's a rollover of a offset distribution so that they will accept it after the normal 60-day rollover deadline for other distributions that are eligible for rollover and so that they record the rollover correctly.
"Then what are your thoughts on rolling the balance over, then taking out a new loan from the new 401k, and then rolling over that money into an IRA?"
You are not the first person to propose this. This is perfectly reasonable if your new plan accepts rollovers and allows loans. You would be completing the rollover of the offset distribution by using the cash that you get from taking out the new loan. Yes, you would be limited to a 5-year repayment period. (I assume that the original loan was for the purchase of a home which permits a payback period longer than 5 years.)
